Polar coordinates to rectangular coordinates?

Question

help!! I need to know how to change tan of theta = r cos of theta -2 to rectangular coordinates and also I need help understanding the concept!!!

Answer 1

All you need to know are the relationships between x,y and r,theta. For simplicity, I'll write theta as t.

x = rcost ... (1)

y = rsint ... (2)

tant = y/x ... (3)

r^2 = x^2 + y^2 ... (4)

In your case, you just need to substitute (1) and (3) into the given equation to get y/x = x - 2.

Answer 2

I) the standard form of rectangular coordinate is a+bi or (a,b)

a is the real part and b is the imaginary part

II) the same cordinates in polar form is (rcost +i rsint)

where r is the hypotenous, a= rcost and b=rsint

Now, your qs

tant = rcost

we have to convert them in terms of 'a' and ' b'

sint /cost = a...........>.(rcost =a and tant = sint/cost)

multiply r to nr and de of LHS

r sint/ r cost = a

b/a = a

a^2 = b

this is how we changed the polar form to rectangular form.